Relative humidity-dependent viscosity of secondary ...

Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-14, 2016 Manuscript under review for journal Atmos. Chem. Phys. Published: 29 January 2016 c Author(s) 2016. CC-BY 3.0 License.

1

Relative humidity-dependent viscosity of secondary organic

2

material

3

implications for organic particulate matter over megacities

from

toluene

photo-oxidation

and

possible

4 5

M. Song1,2, P. F. Liu3, S. J. Hanna1, R. A. Zaveri4, K. Potter5, Y. You1, S. T. Martin3,6, A.

6

K. Bertram1

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[1] {Department of Chemistry, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada}

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[2] {Department of Earth and Environmental Sciences, Chonbuk National University, Jeollabuk-

9

do, Republic of Korea} 

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[3]{John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge,

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Massachusetts 02138, USA}

12

[4]{Atmospheric Sciences and Global Change Division, Pacific Northwest National Laboratory,

13

Richland, WA, USA}

14

[5]{School of Chemistry, University of Bristol, Bristol, UK BS8 1TS, UK}

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[6]{Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts

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02138, USA}

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Correspondence to: A. K. Bertram ([email protected])

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Abstract

20

To improve predictions of air quality, visibility, and climate change, knowledge of the viscosities

21

and diffusion rates within organic particulate matter consisting of secondary organic material

22

(SOM) is required. Most qualitative and quantitative measurements of viscosity and diffusion rates

23

within organic particulate matter have focused on SOM particles generated from biogenic VOCs

24

such as α-pinene and isoprene. In this study, we quantify the relative humidity (RH)-dependent

25

viscosities at 295 ± 1 K of SOM produced by photo-oxidation of toluene, an anthropogenic VOC.

1


−1

6

1

The viscosities of toluene-derived SOM were 2 × 10 to ∼ 6 × 10 Pa·s from 30 to 90% RH, and

2

greater than ~2 × 108 Pa·s (similar to or greater than the viscosity of tar pitch) for RH  17%. These

3

viscosities correspond to Stokes-Einstein-equivalent diffusion coefficients for large organic

4

molecules of ~2 × 10-15 cm2·s-1 for 30% RH, and lower than ~3 × 10-17 cm2·s-1 for RH  17%.

5

Based on these estimated diffusion coefficients, the mixing time of large organic molecules within

6

200 nm toluene-derived SOM particles is 0.1 - 5 hr for 30% RH, and higher than ~100 hr for RH

7

 17%. These results were used, as a first-order approximation, to estimate if organic particulate

8

matter will be in well-mixed over the world’s top 15 most populous megacities. If the organic

9

particulate matter in the megacities is similar to the toluene-derived SOM in this study, in Kolkata,

10

Istanbul, Dhaka, Tokyo, Shanghai, and Mumbai, mixing times in organic particulate matter during

11

extended periods of the year will be very short, and well-mixed particles can be assumed. On the

12

other hand, the mixing times of large organic molecules in organic particulate matter in Delhi,

13

Beijing, Mexico City, Cairo, and Karachi may be long and the particles may not be well-mixed in

14

the afternoon (3:00 – 5:00 local time) during certain times of the year.

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1 Introduction

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Volatile organic compounds (VOCs) are released into the atmosphere from both biogenic and

18

anthropogenic sources. In the atmosphere, VOCs can form secondary organic material (SOM)

19

through oxidation reactions with OH radicals, NO3 radicals, and O3. SOM accounts for 20 – 80%

20

of the mass of organic atmospheric particulate matter at various locations (Zhang et al., 2007;

21

Jimenez et al., 2009). SOM typically consist of thousands of different compounds, and only 10 –

22

20% of the individual molecules that make up SOM particles have been identified (Decesari et al.,

23

2006; Hallquist et al., 2009). The lack of information on the chemical composition of SOM has

24

resulted in a poor understanding of their physical properties, including the viscosity and molecular

25

diffusion rates within SOM particles.

26

Knowledge of the viscosity and molecular diffusion rates within SOM particles is needed to predict

27

the properties of these particles and understand their role in the atmosphere. For example, the size

28

distribution and mode diameter depend on the diffusion rates of organic molecules within the

29

particles (Riipinen et al., 2011; Zaveri et al., 2014). Simulations show that total SOM mass

2


1

concentrations can be overestimated or underestimated depending on what diffusion rates are used

2

(Shiraiwa and Seinfeld, 2012). Chemical aging of atmospheric particles by heterogeneous

3

reactions can depend on diffusion rates within SOM (Shiraiwa et al., 2011; Kuwata and Martin,

4

2012; Zhou et al., 2013; Steimer et al., 2014; Houle et al., 2015) and heterogeneous ice nucleation

5

may be influenced by the viscosity of SOM particles (Murray et al., 2010; Wang et al., 2012;

6

Ladino et al., 2014; Schill et al., 2014; Wilson et al., 2012). Moreover, long-range transport of

7

polycyclic aromatic hydrocarbons can depend on diffusion rates in a particle (Zelenyuk et al., 2012;

8

Zhou et al., 2013) and the efflorescence of crystalline salts can be hindered for highly viscous

9

SOM (Murray, 2008; Murray and Bertram, 2008; Bodsworth et al., 2010; Song et al., 2013).

10

Most qualitative and quantitative measurements of viscosity and diffusion rates within organic

11

particulate matter have focused on SOM generated from biogenic VOCs such as α-pinene and

12

isoprene (Virtanen et al., 2010; Cappa et al., 2011; Perraud et al., 2012; Saukko et al., 2012;

13

Abramson et al., 2013; Robinson et al., 2013; Renbaum-Wolff et al., 2013a; Bateman et al., 2015;

14

Kidd et al., 2014; Pajunoja et al., 2014; Wang et al., 2014; Song et al., 2015). Recently, the

15

viscosity and diffusion rates within SOM particles generated from anthropogenic VOCs have also

16

been investigated. Using single particle mass spectrometry, Robinson et al. (2013) investigated

17

mixing of toluene-derived SOM particles and SOM particles from -pinene ozonolysis. One

18

possible explanation of the lack of mixing within toluene-derived SOM particles was a high

19

viscosity of the SOM. From bounce experiments, Saukko et al. (2012) reported that SOM particles

20

derived from naphthalene and n-heptadecane are highly viscous upon increasing oxidation. Also

21

from bounce experiments, Bateman et al. (2015) showed SOM derived from photo-oxidation of

22

toluene had a viscosity > 100 Pa·s for relative humidity (RH) values < 80%. Li et al. (2015)

23

showed through bounce experiments that SOM derived from m-xylene and 1,3,5-trimethylbenzene

24

had a viscosity of > 100 Pa·s at RH values less than 70%. Li et al. (2015) also used results of

25

reactive uptake studies to infer that for RH values of 35 - 45% the diffusion coefficient of

26

carboxylic acids within SOM generated from several anthropogenic VOCs (toluene, m-xylene and

27

1,3,5-trimethylbenzene) was 3×10-18

28

measuring the viscosity and diffusion rates within SOM generated from anthropogenic VOCs,

29

additional studies are needed to quantify the viscosities and diffusion rates over the full range of

30

RH found in the atmosphere.

± 0.5

m2 s-1. Although there has been recent progress in

3


1

In the following, we measure the viscosities of toluene-derived SOM over the range of RH values

2

found in the atmosphere. As in previous studies, SOM from the photo-oxidation of toluene serves

3

as a proxy for organic particulate matter from anthropogenic sources in megacities (e.g. Pandis et

4

al., 1992; Robinson et al., 2013). After determining viscosities as a function of RH, the Stokes-

5

Einstein equation is used to convert the viscosities into equivalent diffusion rates of large organic

6

molecules within toluene-derive SOM. The Stokes-Einstein equation should give reasonable

7

values of diffusion rates when the viscosity is not near the viscosity of a glass (~1012 Pa s) and

8

when the molecules are roughly the same size or larger than the molecules in the SOM matrix

9

(Champion et al., 2000; Koop et al., 2011; Shiraiwa et al., 2011; Power et al., 2013). Finally, the

10

results are used to estimate the viscosities and diffusion rates in organic particulate matter over

11

megacities.

12 13

2 Experimental

14

The production and collection of SOM particles onto hydrophobic substrates (which are needed

15

for the beam mobility and poke-and-flow experiments) is discussed in Sect. 2.1. The viscosity of

16

toluene-derived SOM was determined using the bead-mobility technique and the poke-flow

17

technique together with simulations of fluid flow. These two techniques are discussed in Sects. 2.2

18

and 2.3.

19

2.1 Production and collection of secondary organic material on hydrophobic

20

substrates

21

SOM aerosols particles having diameters less than 1 m were generated by toluene photo-

22

oxidation in an oxidation flow reactor (OFR) (Kang et al., 2007; Lambe et al., 2011). The

23

procedure for generating SOM from toluene photo-oxidation in the flow reactor has been given by

24

Liu et al. (2013). Only the details relevant to the current experiments are given here.

25

For this study, the volume of the OFR was 13.3 L and the reactor was operated at a flow rate of

26

~7 L m-1 with a residence time in the range of ~ 110 s. The temperature used in the OFR

27

experiments was 293 ± 2 K and the concentrations of toluene and ozone used in the flow reactor

28

are listed in Table 1. Ozone was produced external to the flow reactor by irradiating pure air with

4


1

the ultraviolet emission from an Hg lamp (λ = 185 nm). The injected ozone concentration was ~30

2

ppm. Hydroxyl radicals were produced inside the OFR by the following photochemical reactions:

3

O3 + hν (λ = 254 nm)

4

O(1D) + H2O

5

Mass concentrations of SOM particles in the OFR were 60-100 μg m-3 and 600-1000 μg m-3 for

6

the two different experimental conditions (see Table 1). At the outlet of the OFR, two different

7

methods were used for the collection of SOM particles. In the first method, SOM particles were

8

collected on a hydrophobic slide using an electrostatic precipitator (TSI 3089, USA). After

9

collection, the SOM particles on the hydrophobic slides, formed from coalescence during sampling,

10

were smaller than ~5 µm in diameter. For the bead-mobility and poke-flow techniques, however,

11

particle sizes between 20 - 60 µm in diameter are needed. To generate these large sizes, the

12

hydrophobic slides containing the SOM particles were placed inside an RH- and temperature-

13

controlled flow cell (Pant et al., 2006; Bertram et al., 2011; Song et al., 2012) and the RH was

14

increased to > 100%. This procedure caused particle growth by water uptake and eventual

15

coagulation among particles. This growth and coagulation process resulted in larger but fewer

16

SOM particles on the hydrophobic slides. Details of this procedure are given by Renbaum-Wolff

17

et al. (2015) and Song et al. (2015). This procedure was used for samples 1, 2, 5, and 6 shown in

18

Table 1.

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In the second method, SOM particles were collected on hydrophobic surfaces using a single stage

20

impactor (Prenni et al., 2009; Poschl et al., 2010). During impaction, the collected submicron SOM

21

particles coagulated, resulting in particles with sizes between 10 and 100 µm in diameter. These

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supermicron particles were used directly in the bead-mobility and poke-flow experiments. This

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procedure was used to collect samples 3, 4, 7, and 8 shown in Table 1.

24

For all the bead-mobility experiments, a Teflon substrate was used. For all the poke-and-flow

25

experiments, hydrophobic glass slides coated with trichloro(1H,1H,2H,2H-perfluorooctyl)silane

26

(Sigma-Aldrich) were used. The coating procedure is described in Knopf (2003).

27

2.2 Bead-mobility experiments

O2 + O(1D)

(R1),

2OH

(R2)

5


1

The bead-mobility technique was previously described in Renbaum-Wolff et al. (2013a, b). Briefly,

2

a water suspension of ~1 μm insoluble melamine beads (Sigma Aldrich Cat. #86296) was

3

nebulized and incorporated into supermicron SOM particles deposited on a hydrophobic substrate

4

(toluene samples 1-4, Table 1). The hydrophobic substrate with the SOM particles and beads was

5

placed in a flow-cell with variable RH and a temperature of 295 ± 1 K. A continuous flow of

6

N2/H2O gas (flow rate  1200 sccm) was passed over the supermicron particles. The flow above

7

the particles resulted in a shear stress on the particle surface and internal circulations within the

8

particle, which could be visualized by observing the beads within the particles with a light-

9

transmitting microscope coupled to a CCD camera (Zeiss Axio Observer, magnification 40).

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Figure 1 shows images from a typical bead-mobility experiment for a toluene-derived SOM

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particle at 80% RH. Typically, 1 to 7 beads were monitored within a particle over 50 - 100 frames.

12

The time between frames ranged from 0.2 s – 10 min depending on the velocity of the beads. From

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the location of the beads as a function of time, the speed of individual beads was determined. These

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individual speeds were then used to determine average bead speeds for a given sample and RH.

15

The measured speeds of 3 - 10 beads were used to determine a mean bead speed. Bead speeds were

16

not reported at RH < 60% since at these RH values the movements of the beads were too slow to

17

measure for typical observation times.

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The average bead speed for a given sample and RH was converted to viscosity using a calibration

19

line. The calibration line was developed by Song et al. (2015) from measurements of bead speed

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in sucrose-water particles over a range of RH values. The RH within the flow-cell was measured

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using a hygrometer with a chilled mirror sensor (General Eastern, Canada), which was calibrated

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by measuring the deliquescence RH for pure ammonium sulfate particles (80.0% RH at 293 K,

23

Martin (2000)). The uncertainty of the hygrometer was ± 0.5% RH after calibration.

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2.3 Poke-flow technique in conjunction with fluid simulation

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The poke-and-flow technique in conjunction with fluid simulations was used to measure the

26

viscosities of SOM particles at RH values less than 50%. This technique was not used at RH values

27

> 50% since the flow rates of the SOM after poking were too fast to observe at these RH values.

28

The qualitative method of poking an inorganic particle to determine its phase (i.e., solid or liquid)

29

was introduced by Murray et al. (2012). Renbaum-Wolff et al. (2013a) and Grayson et al. (2015a)

30

expanded on this method by measuring the characteristic flow time of a material after poking and

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1

extracting viscosity information from simulations of fluid flow. Briefly, supermicron toluene-

2

derived SOM particles deposited on a hydrophobic substrate (Toluene 5 to 8, Table 1) were placed

3

inside a flow-cell with RH control. The particles were conditioned for 30 min at > 70% RH, 60

4

min at 60 – 70% RH, 2 h at 30 – 60% RH, and 3 h at ≤ 30% RH. These times are sufficient for the

5

particles to equilibrate with the surrounding water vapor based on recent measurements of

6

diffusion coefficients of water within SOM (Price et al., 2015). After equilibration, particles were

7

poked using a sharp needle (0.9 mm × 40 mm) (Becton-Dickson, USA) that was mounted to a

8

micromanipulator (Narishige, model MO-202U, Japan) and inserted through a small hole in the

9

top of the flow-cell. The geometrical changes before, during, and after poking a particle were

10

recorded by a reflectance optical microscope (Zeiss Axio Observer, 40× objective) equipped with

11

a CCD camera. At 30 - 50% RH the action of poking the particles with the needle resulted in the

12

material forming a half torus geometry (see Fig. 2a). From the images recorded after poking the

13

particles, the experimental flow time, τexp, flow, was determined. The experimental flow time was

14

defined as the time taken for the equivalent-area diameter of the inside of the half torus geometry

15

to reduce to 50% of the initial diameter. Here the equivalent-area diameter, d, is calculated as d =

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(4A/π)1/2 where A represents the hole area (Reist, 1992). For RH < 20% the SOM particles shattered

17

after poking, and no restorative flow was observed over ~5 hr (See Fig. 2b). In this case τexp, flow

18

was set to > 5 hr.

19

To determine viscosities from τexp, flow, simulations of fluid flow were carried out with the finite-

20

element analysis software package, COMSOL Multiphysics (Renbaum-Wolff et al., 2013a;

21

Grayson et al., 2015a). The mesh size used in the simulations was 4.04 – 90.9 nm. The physical

22

parameters (i.e., slip length, surface tension, contact angle, and density) used in the simulation are

23

listed in Table 2.

24

For each particle for which flow was observed, simulations were run using a half torus geometry,

25

similar to the geometry observed in the experiments where flow was observed. The radius of the

26

tube, R, in the half torus geometry and the radius of the hole, r, in the half torus geometry used in

27

the simulations were based on the images recorded immediately after poking the particles with the

28

needle. To determine viscosity for each particle, viscosity in the simulations was adjusted until

29

τmodel, flow was within 1% of τexp, flow.

30

In cases for which the particles cracked, simulations were run using a quarter-sphere model with

31

one of the flat faces of the quarter sphere in contact with the substrate, similar to what was observed

7


1

in the experiments (Renbaum-Wolff et al., 2013a). The diameter used for the quarter sphere was

2

20 µm. In this case we determined a lower limit to the viscosity by adjusting the viscosity in the

3

simulation until the sharp edge of the quarter sphere model moved by 0.5 µm within 5 hr. A value

4

of 0.5 µm was used since this amount of movement could be observed in the optical microscope

5

experiments.

6 7

3 Results

8

Shown in Fig. 3 are the mean bead speeds of individual SOM samples (toluene 1, 2, 3, and 4)

9

measured at different RH values between 60 and 90% RH (see Sect. 2.1). As the RH decreased

10

from 89.9 to 60.7%, the average bead speed decreased by a factor of 22 from 9.20  10-4 to 4.24 

11

10-7 μm·ms-1. Sample-to-sample variation was less than the uncertainty in the measurements and,

12

within uncertainty, the results for 60 - 100 µg·m-3 concentration agreed with the results for 600 -

13

1000 µg·m-3 concentration.

14

Figure 4 shows the result of τexp, flow as a function of RH for the different samples (toluene 5, 6, 7,

15

and 8). The τexp, flow increased from ~1 s to ~2000 s as RH decreased from 50 to 30% RH. The τexp,

16

flow

17

with mass concentrations over the range studied (600-1000 and 60-100 µg·m-3), as shown in Fig.

18

4.

19

Shown in Fig. 5 are the viscosities as a function of RH for toluene-derived SOM particles

20

determined from the bead-mobility experiments (Sect. 2.2) and the poke-flow experiments in

21

conjunction with the fluid simulation (Sect. 2.3). For the bead-mobility experiments, the viscosities

22

were determined by the mean of bead speeds between 60 and 90% RH. The y-error bars indicate

23

the 95% prediction intervals from the calibration line (Song et al., 2015). The x-error bars represent

24

the uncertainty in the RH measurements. The viscosity of the SOM increases from ~0.2 to ~129

25

Pa·s as RH decreases from 89.9 to 60.7%. As shown in Fig. 5, difference between the results for

26

the 600-1000 and 60-100 µg·m-3 samples are less than the uncertainties in the measurements.

27

Also shown in Fig. 5 are the calculated viscosities of the toluene-derived SOM for RH < 50% from

28

the poke-flow experiments. The viscosity increases from approximately 7.8 × 103 to 6.3 × 106 Pa·s

variation from sample to sample was less than the variation within individual toluene samples

8


1

as RH decreases from 47.3 to 30.5%. The uncertainty in the viscosity of approximately two orders

2

of magnitude arises from the uncertainties in the physical parameters used in the simulations. For

3

RH < 20%, restorative flow did not occur over ~5 hrs resulting in a lower limit to the viscosity of

4

~2 × 108 Pa·s, similar to or greater than the viscosity of tar pitch (~10 8 Pa·s, Koop et al. (2011)).

5 6

4 Discussion

7

Bateman et al. (2015) previously estimated the viscosity of toluene-derived SOM from particle

8

rebound experiments. From their measurements they estimated a viscosity of 100 to 1 Pa·s for

9

RHs between 60 and 80% with SOM mass concentrations of 30 - 50 μg·m-3 (green box in Fig. 5)

10

in good agreement with our measurements.

11

Li et al. (2015) previously estimated the diffusion coefficient of carboxylic acids within toluene-

12

derived SOM from measurements of reactive uptake of NH3. They estimated a diffusion

13

coefficient 10-17.5±0.5 m2·s-1 for RHs between 35 and 45% using SOM mass concentrations of 44 to

14

125 μg m-3. If a hydrodynamic radius of 0.1 - 1.5 nm is assumed (Li et al., 2015), viscosity of 1 

15

104 – 2  106 Pa·s is calculated using the Stokes-Einstein equation (blue box in Fig. 5), consistent

16

with our measurements. The good agreement between the current results and the results from

17

Bateman et al. and Li et al. suggests that the viscosity of the toluene-derived SOM is relatively

18

insensitive to the particle mass concentrations at which the SOM is produced over the range of 30

19

to 1000 μg·m-3.

20

A liquid is defined as a material with a viscosity less than 10 2 Pa·s; a semisolid is defined as a

21

material with a viscosity between 102 Pa·s and 1012 Pa·s; and a solid is defined as a material with

22

a viscosity greater than 1012 Pa·s (Koop et al., 2011; Shiraiwa et al., 2011). As shown in Fig. 5,

23

the viscosities of the SOM produced from toluene photo-oxidation correspond to liquid for RH >

24

60%, a semisolid for 60% < RH < 30%, and a semisolid or a solid for RH < 20%. Our results

25

suggest a semisolid-to-liquid phase transition at an RH between 60 and 70%, in good agreement

26

with Bateman et al. (2015) who suggested a semisolid-to-liquid phase transition of toluene-derived

27

SOM particles in the range of 60 - 80% RH.

9


1

From the viscosities determined at 295 ± 1 K and the Stokes-Einstein relationship (assuming a

2

hydrodynamic radius of 0.4 nm for organic molecules within the toluene-derived SOM, Renbaum-

3

Wolff et al., 2013a), we calculated the diffusion coefficients of large organic molecules, Dorg,

4

within toluene-derived SOM (see secondary y-axis in Fig. 5). Dorg ranges from ~3 × 10-8 to ~2 ×

5

10-15 cm2·s-1 for RH from 90 to 30%. It is lower than ~3 × 10-17 cm2·s-1 for RH  17%. The Stokes-

6

Einstein relation is not expected to predict with high accuracy the diffusion rates of small gas

7

molecules such as OH, O3, NOx, NH3, and H2O (Koop et al., 2011; Shiraiwa et al., 2011). However,

8

the Stokes-Einstein relationship should give reasonable estimations of diffusion rates for large

9

organic molecules for conditions not close to the glass transition temperature of the matrix

10

(Champion et al., 2000; Koop et al., 2011; Shiraiwa et al., 2011; Power et al., 2013). However, the

11

relationship may be inaccurate near the glass transition RH (Champion et al., 2000; Shiraiwa et al.,

12

2011; Power et al., 2013).

13

Using the diffusion coefficients (Dorg), the mixing time by diffusion, τmixing, of large organic

14

molecules within a 200 nm SOM particle was calculated with the following equation, where d is

15

the particle diameter (Shiraiwa et al., 2011; Bones et al., 2012; Renbaum-Wolff et al., 2013a):

16

𝜏𝑚𝑖𝑥𝑖𝑛𝑔 =

17

Here we are using 200 nm to represent a typical accumulation mode atmospheric particle, Shiraiwa

18

et al. (2011). The concentration of the diffusing molecules anywhere in the particles deviates by

19

less than e-1 from the homogeneously well-mixed case at times longer than τmixing. The τmixing values

20

calculated with this procedure are indicated in Fig. 5 (secondary y-axis). At an RH of 45% or

21

higher, the mixing times are short, approaching less than or equal to 0.1 h. At 30% RH the mixing

22

times are between 0.1 and 5 h. At RH  17% the mixing time is longer than ~100 h.

𝑑2

(Eq.1)

4π2 𝐷𝑜𝑟𝑔

23 24

5 Atmospheric implications

25

In the following, we use the mixing times calculated in the previous section to estimate the mixing

26

times of large organic molecules in organic particulate matter over megacities. Several caveats

27

should be kept in mind when applying the mixing times discussed earlier to particles over

28

megacities. First, we are assuming that toluene-derived SOM is a good proxy for organic

10


1

particulate matter over megacities. Organic particulate matter over megacities are most likely more

2

complicated and may include inorganic components. Second, the toluene-derived SOM was

3

generated using relatively large mass concentrations of particles (60 – 1000 μg·m-3). The good

4

agreement between our results and the results from Bateman et al. (2015) and Li et al. (2015),

5

which were carried out with a mass concentration of 30 – 1000 μg·m-3, suggests that for toluene-

6

derived SOM the viscosity is not strongly dependent on the mass concentration of organics used

7

to generated the SOM, but additional studies are needed to confirm this. Third, as mentioned above,

8

the Stokes-Einstein equation was used to estimate diffusion coefficients and hence mixing times,

9

and this equation can underestimate diffusion coefficients close to the glass transition temperature.

10

Despite these caveats, our estimates below should be a useful first-order approximation to the

11

mixing times of large organics in organic particulate matter over megacities.

12

For this analysis we define megacity as a metropolitan area with a total population in excess of ten

13

million people. Based on the Population Division Data Query (2014) of the United Nations

14

(http://esa.un.org/), we selected the top 15 most populous cities (Tokyo, Delhi, Shanghai, Mexico

15

City, São Paulo, Mumbai, Osaka, Beijing, New York, Cairo, Dhaka, Karachi, Buenos Aires,

16

Kolkata, and Istanbul) which meet this criterion.

17

In order to determine τmixing for organic particulate matter in megacities, information on the RH in

18

the cities is needed. Fig. 6 gives information on RH and temperature in the 15 most populous

19

megacities obtained from NOAA’s National Climatic Data Center (NCDC) (www.ncdc.noa.gov).

20

The figure shows boxplots of average afternoon (3:00 – 5:00 local time) RH and temperature from

21

these cities for the years from 2004 – 2014. The afternoon (3:00 – 5:00 local time) was chosen for

22

this analysis since this is the time of day when RH is typically the lowest. In the figure, the boxes

23

represent the median, 25th and 75th percentiles and the whiskers show the 10th and 90th percentiles.

24

In the Fig. 6, we indicate with green shading cases when the afternoon RH (at the 10th percentile

25

level) does not go below 45% RH. The cases when the afternoon RH (at the 10th percentile level)

26

does not go below 45 % RH are listed in Table 3 (second column). At 45% RH the mixing time

27

within toluene-derived SOM is short (i.e., less than or equal to 0.1 h). Figure 6 (green shading)

28

and Table 3 suggests that, if the organic particulate matter over megacities is similar to the toluene-

29

derived SOM in this study, in Kolkata, Istanbul, Dhaka, Tokyo, Shanghai, and Mumbai, mixing

11


1

times during extended periods of the year will be very short, and homogeneously well-mixed

2

particles can be assumed.

3

In the Fig. 6, we indicate with red shading cases where the afternoon RH (at the 10 th percentile

4

level) is 17% or lower. The cases when the afternoon RH (at the 10th percentile level) is 17 % or

5

lower are listed in Table 3 (third column). As mentioned above, at this RH, the mixing time within

6

toluene-derived SOM is long (> 100 h), based on the viscosity measurements and Stokes-Einstein

7

calculations. Fig. 6 (red shading) and Table 3 (third column) suggests that if the organic particulate

8

matter is similar to the toluene-derived SOM in this study, in Delhi, Beijing, Mexico City, Cairo,

9

and Karachi, the particles may not be well-mixed in the afternoon (3:00 – 5:00 local time) during

10

certain times of the year. If the breakdown to the Stokes-Einstein relationship is large at high

11

viscosities the number of cases classified as having particles not well-mixed may be less than

12

indicated. Hence, the number of cases classified as having particles not well-mixed based on the

13

viscosity data presented here and the Stokes-Einstein relationship should be considered as an upper

14

limit.

15

Another caveat to the discussion above is the effect of temperature on viscosity. The conclusions

16

reached above were based on viscosity measurements carried out at 295 ± 1 K, while the

17

temperatures shown in Fig. 6 ranges from roughly 0 C to 40 C. Viscosity is known to decrease

18

as the temperature increases, but the effect of temperature on the viscosity of SOM has not been

19

quantified. Studies that quantify the effect of temperature on the viscosity of SOM are needed for

20

more accurate predictions of the mixing times in organic particulate matter over megacities.

21

Kleinman et al., (2009) studied the time evolution of aerosol size distributions and number

22

concentrations of ambient particulate matter over the Mexico City plateau during the MILAGRO

23

(Megacity Initiative: Local And Global Research Observations) field campaign conducted in

24

March 2006. The particulate matter over Mexico City was primarily organic and as photochemical

25

aging occurred, Kleinman and colleagues observed an increase in accumulation-mode volume due

26

to an increase in the accumulation mode particles, not because of an increase in the average size

27

of the accumulation mode. The condensing organic vapors from photooxidation of toluene and

28

other anthropogenic VOCs over Mexico City are expected to be semivolatile (Shrivastava et al.,

29

2013). However, Kleinman et al. showed that the observed evolution of aerosol size distribution

30

was not consistent with a volume growth mechanism in which the semivolatile organic vapors are

12


1

expected to readily diffuse within the accumulation mode substrate. This could indicate that the

2

accumulation mode particles over Mexico City were highly viscous and did not reach equilibrium

3

with large gas-phase organic molecules during the observation period. This observation is

4

consistent with our experimental results that toluene-derived SOM is highly viscous at RH < 20%

5

and Fig. 6, which shows that the median RH in Mexico City often falls below 20% in March.

6

However, it should be noted that the particulate matter over Mexico City is likely more chemically

7

complex than the SOM used in this study.

8 9

6 Conclusions

10

We investigated the RH-dependent viscosities at room temperature of SOM particles produced

11

from toluene photo-oxidation with the mass concentration of 60 – 1000 μg·m-3. A bead-mobility

12

technique showed the viscosities of the toluene-derived SOM increased from ~0.2 to ~129 Pa·s as

13

RH decrease from 89.9 to 60.7%. This indicates that the toluene-derived SOM particles are a liquid

14

at RH > 60%. The RH range for liquid-to-semisolid is in good agreement with Bateman et al.

15

(2015) who showed the liquid-to-semisolid phase transition of these particles in the range of 60-

16

80% RH. A poke-flow technique combined with fluid simulations showed the viscosities increased

17

from approximately 7.8 × 103 to 6.3 × 106 Pa·s as RH decreases from 47.3 to 30.5%. For RH 

18

17%, the viscosities of the SOM were greater than or equal to ~2 × 108 Pa·s, similar to or greater

19

than the viscosity of tar pitch. This suggests that the toluene-derived SOM particles are a semisolid

20

at 20 < RH  60%, and a semisolid or a solid at RH  17%. Using the viscosity data and the Stokes-

21

Einstein equation, the diffusion coefficients of large gas-phase organic molecules within the

22

toluene-derived SOM particles were calculated to be ~3 × 10-8 to ~2 × 10-15 cm2 s-1 for RHs from

23

89.9 to 30.5%, and is lower than ~3 × 10-17 cm2 s-1 for RH  17%. Mixing time by diffusion of

24

large organic molecules within 200 nm toluene-derived SOM particles was calculated to be less

25

than 0.1 h at RH < 47.3%, 0.5 - 5 h at 30.5% RH, and greater than ~ 100 h at RH  17%.

26

To apply the results of the viscosities, diffusion coefficients, and mixing time of the toluene-

27

derived SOM, we selected the top 15 most populous megacities. Based on the RH in the cities, and

28

if the organic particulate matter in megacities is similar to the toluene-derived SOM in this study,

29

in cities such as Kolkata, Istanbul, Dhaka, Tokyo, Shanghai, and Mumbai, mixing times during

13


1

extended periods of the year will be very short and homogeneously well-mixed particles can be

2

assumed. On the other hand, for certain times of the year in Delhi, Beijing, Mexico City, Cairo,

3

and Karachi, mixing times of large organic molecules in organic particulate matter may be long (

4

100 hr), and the particles may not be well mixed in the afternoon (3:00 – 5:00 local time) during

5

certain times of the year. These results are summarized in Fig. 7.

6 7

Acknowledgments

8

This work was supported by the Natural Sciences and Engineering Research Council of Canada.

9

Support from the USA National Science Foundation, the Atmospheric Science Research (ASR)

10

Program of the USA Department of Energy, and research funds for newly appointed professors of

11

Chonbuk National University in 2015 is also acknowledged.

12 13

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23


1

Table 1. Experimental conditions for production and collection of toluene-derived SOM particles

2

using the oxidation flow reactor. Particles were collected onto hydrophobic substrates using an

3

electrostatic precipitator or a single stage impactor. SOM sample name

Toluene conc.

Ozone conc.

(ppm)

(ppm)

SOM mass OFR flow Collection conc. during rate time production (L m-1) (hr) -3 (μg m )

Collection method

For bead-mobility experiments Toluene 1

1.0 ± 0.1

30 ± 3

600-1000

7.0 ± 0.5

48

Electrostatic precipitator

Toluene 2

1.0 ± 0.1

30 ± 3

600-1000

7.0 ± 0.5

48


Toluene 3

0.1 ± 0.01 30 ± 3

60-100

7.0 ± 0.5

12

Impactor

Toluene 4

0.1 ± 0.01 30 ± 3

60-100

7.0 ± 0.5

19

Impactor

For poke-flow experiments Toluene 5

1.0 ± 0.1

30 ± 3

600-1000

7.0 ± 0.5

96


Toluene 6

1.0 ± 0.1

30 ± 3

600-1000

7.0 ± 0.5

96


Toluene 7

0.1 ± 0.01 30 ± 3

60-100

7.0 ± 0.5

12.5

Impactor

Toluene 8

0.1 ± 0.01 30 ± 3

60-100

7.0 ± 0.5

16

Impactor

4 5

24


1

Table 2. Physical parameters used to simulate material flow in the poke-flow experiments. R and

2

r indicate the radius of a tube and the radius of an inner hole, respectively. Slip length

Surface tension

Density

Contact angle

(nm)

(mN m-1)

(g cm-3)

(°)

Values used to calculate 5a lower limit

28b

1.4c

80 (if r < 2R),

Values used to calculate 10000a upper limit

75d

100 (if r > 2R) 1.4c

80 (if r < 2R), 100 (if r > 2R)

3

a

4

literature data (Schnell, 1956; Churaev et al., 1984; Watanabe et al., 1999; Baudry et al., 2001;

5

Craig et al., 2001; Tretheway and Meinhart, 2002; Cheng and Giordano, 2002; Jin et al., 2004;

6

Joseph and Tabeling, 2005; Neto et al., 2005; Choi and Kim et al., 2006; Joly et al., 2006; Zhu et

7

al., 2012; Li et al., 2014).

8

b

9

the surface tension of liquid toluene at 293 K (Adamson and Gast, 1997).

The range of slip length, which is the interactions between fluids and solid surfaces, is based on

The lower limits of the surface tension of toluene-derived SOM were determined as 28 mN m-1,

10

c

Ng et al., 2007

11

d

The upper limits of the surface tension of toluene-derived SOM were determined as 75 mN m-1,

12

the surface tension of pure water at 293 K (Engelhart et al., 2008).

13

e

14

microscope ranged from 80 - 100°. The relationship of viscosity and contact angle depends on the

15

ratio of the radius of a tube, R, to the radius of an inner hole, r (Grayson et al., 2015a).

Contact angle of the toluene-derived SOM on a substrate measured by 3-D fluorescence confocal

16

25


1

Table 3. Months when the afternoon RH in the 15 most populous megacities either does not go

2

below 45 % (at the 10th percentile level) or is 17% or lower (at the 10th percentile level). “None”

3

indicates the RH does not meet either of these criteria. Megacity

Tokyo Delhi Shanghai Mexico City Sao Paulo Mumbai Osaka Beijing New York Cairo Dhaka Karachi Buenos Aires Kolkata Istanbul

Months when the afternoon RH (at the 10th percentile level) does not go below 45 % Jun. – Sep. none Jun. – Sep. none Jan. May – Sep. Jul. none none none Jun. – Oct. Jun. – Aug. none May – Oct. Jan. – Feb., Oct. – Dec.

4

26

Months when the afternoon RH (at the 10th percentile level) is 17 % or lower none Mar. – Jun. none Jan. – May, Dec. none none none Jan. – May, Nov. – Dec. none Mar. – May none Jan. – Apr., Oct. – Dec. none none none


1

2 3

Fig. 1. Optical images from typical bead-mobility experiments for a toluene-derived SOM particle

4

(Toluene sample 8 in Table 1) at 80% RH. Three different beads are labeled using colored arrows.

5

The x and y coordinates of these beads are also indicated. Scale bar: 20 µm.

6 7

27


1 2 3

Fig. 2. Optical images of pre-poking, poking, and post-poking from typical poke-flow experiments

4

on toluene-derived SOM particles (toluene sample 6) at (a) 39.5% RH and (b) 16.5% RH. Panel

5

a1 and b1; pre-poking, Panel a2 and b2: post-poking immediately after the needle has been

6

removed (time set = 0 s), Panel a3; the experimental flow time, τ exp, flow, where the diameter of hole

7

has decreased to 50% of its initial size, and Panel b3; particles shatter and do not flow over a period

8

of 6.5 h. Size bar: 20 µm.

9 10 11 12 13 14 15

28


1 2 3

Fig. 3. Measured average bead speeds as a function of RH for different SOM samples (Toluene 1,

4

2, 3, and 4, see Table 1). The bead speeds of 3 - 10 beads were used to determine a mean bead

5

speed. The x-error bars represent the uncertainty in the RH measurements and the range of RH

6

values in a given experiment. The y-error bars represent the standard deviation of the measured

7

bead speeds.

8

29


1 2 3

Fig. 4. Results from poke-flow experiments. τexp, flow, where the diameter of hole has decreased to

4

50% of its initial size, measured for the different samples (Toluene 5, 6, 7, and 8, see Table 1).

5

The arrows indicate particles shattered at the given RH.

6

30


1 2 3

Fig. 5. Viscosities of toluene-derived SOM particles as a function of RH. For RH > 60% the

4

viscosities were determined from the mean bead speeds (see Fig. 3) and a calibration line (Song et

5

al., 2015). The y-error bars for RH > 60% represent the 95% prediction intervals from the

6

calibration line. For RH < 60% the viscosities were calculated from the τexp, flow where y-error bars

7

represent the calculated lower and upper limits of viscosity using the simulations. The x-error bars

8

over the entire range of RH represent the range of RH values in a given experiments and the

9

uncertainty in the RH measurements. The right y-axes present calculated diffusion coefficients of

10

organic molecules in SOM using the Stoke-Einstein relation, and calculated mixing times within

11

200 nm particles due to bulk diffusion using Eq. (1). The black lines represent linear fits for the

12

RH vs. log(lower viscosities) (R2 = 0.958) and log(upper viscosities) (R2 = 0.984) from the entire

13

data set excluding the RH where particles cracked. Viscosity of toluene-derived SOM particles

14

from Bateman et al. (2015) (green box) and Li et al. (2015) (blue box) is also included.

15

31


1 2 3

Fig. 6. Monthly average RH and temperature for the megacities of Tokyo, Delhi, Shanghai,

4

Mexico City, São Paulo, Mumbai, Osaka, Beijing, New York, Cairo, Dhaka, Karachi, Buenos

5

Aires, Kolkata, and Istanbul. For the stations, afternoon averages RH values (3-5 pm local time)

6

were retrieved from NOAA’s National Climate Data Center for the years from 2004 to 2014. Boxes

7

show the median, 25th and 75th percentiles of 3-hr averages and the whiskers show the 10th and

8

90th percentiles. Green shading indicates that the afternoon RH (at the 10th percentile level) does

32


1

not go below 45% RH. Red shading indicates that the afternoon RH (at the 10th percentile level)

2

is 17% or lower.

3

33


1 2 3

Fig. 7. Summary of conclusions reached after applying the results of the viscosities, diffusion

4

coefficients, and mixing time of the toluene-derived SOM to the top 15 most populous megacities.

5

Green circles indicates megacities where the afternoon RH at 10th percentile does not go below

6

45 % RH for certain times of the year. In these cases, well-mixed particles can be assumed. Red

7

crosses indicates megacities where the afternoon RH at 10th percentile is 17 % or lower for certain

8

times of the year. In these cases, the particles may not be well-mixed in the afternoon for certain

9

times of the year.

34